Scan time is crucial in some applications, such as Cardiac MR and Functional MR. Projection on convex sets (POCS), parallel imaging techniques, and k-t space based reconstruction techniques are independent sets of methods to reduce MRI acquisition time, i.e. by reducing the amount of acquired data in k-space. It is possible to combine one or more of these sets of techniques together.
Recently, some projection on convex sets (POCS) based reconstruction methods have been introduced. These methods can offer a straightforward and computationally efficient way to incorporate non-linear constraints into the reconstruction, which can lead to improved image quality and/or reliable reconstruction for underdetermined problems. Kholmovskil and Samsonov et al. proposed a set of POCS based methods (1–5) for reconstruction with the data for parallel imaging. This set of methods can be referred to as POCSENSE. In these methods, besides partial k-space and sensitivity maps, image support and/or the image phase, which is obtained either from other references or smoothness of initial reconstruction, are utilized as input. POCS is also widely used for non-Cartesian trajectory reconstruction. J. Lee et al. (6) and Moriguchi et al. (7) proposed an application for under-sampled variable-density spiral trajectories. K. J. Lee  et al. applied POCS on radial trajectory (8) and spin-echo EPI (9). Chang and Xiang (10) introduced a hybrid method of Gradient Energy Minimization (GEM) and POCS to reconstruct high quality images with partial k-space but without using phased array coil.
Parallel imaging techniques using multiple coils have become increasingly important since the late 1980's due to higher signal to noise ratios (compared to volume coils or large surface coils) and reduced MRI acquisition time. Some techniques require coil sensitivity maps, such as sensitivity encoding (SENSE) (11), sub-encoding (12) and simultaneous acquisition of spatial harmonics (SMASH)(13). SENSE provides an optimized reconstruction whenever a perfectly accurate coil sensitivity map can be obtained. However, there are some cases where the acquired sensitivity maps contain significant errors. For example, patient motion, including respiratory motion, can lead to substantial errors in acquired sensitivity maps, particularly at the coil edges where the coil sensitivity changes rapidly. Any errors contained in these maps will propagate into the final image during SENSE reconstruction and may also result in decreased signal-to-noise ratios. In such cases, methods utilizing interpolation of k-space data without the use of sensitivity maps might be a better choice.
VD-AUTO-SMASH (14), Generalized Auto calibrating Partially Parallel Acquisitions (GRAPPA) (15), and linear interpolation in k-space (16) are examples of methods that do not use sensitivity maps. Both VD-AUTO-SMASH and GRAPPA use weighted linear combinations and extra k-space lines to interpolate missing k-space data. The extra lines are known as auto-calibration signal lines (ACS lines) and are used to generate the weights used in the linear combinations. VD-AUTO-SMASH interpolates the composite k-space, while GRAPPA interpolates the k-space of individual coils. Some of the drawbacks of VD-AUTO-SMASH are described in detail in reference (15).
Methods of generating images using k-t space based reconstruction techniques can be applied to dynamic imaging. These techniques exploit the temporal correlations among a sequence of images. Such methods include, for example, keyhole (Suga, Mikio, TM Masaru Komori, Kotaro Minato, Takashi Takahashi (1999), “Keyhole Method for High-Speed Human Cardiac Cine MR Imaging”, Journal of Magnetic Resonance Imaging, 10:778–783 (17–19), continuous update with random encoding (CURE), reduced field of view (FOV), and broad-use linear acquisition speed-up technique (BLAST) (Tsao, Jeffrey, Behnia, Babak, Tsao B B, Andrew G. Webb (2001), “Unifying Linear Prior-Information-Driven Methods for Accelerated Image Acquisition”, Magn. Reson. Med., 46:652–660) (20). These methods use the prior information in k-space, which often leads to an artificial view of dynamic area. Underdetermined variable density SENSE (Katscher, U. (2003), “Underdetermined variable density SENSE”, ISMRM, Toronto. p 2342 (21) uses a pre-scan low resolution image as prior information. This method is more general because it can be used for other than dynamic MRI. However, due to the minimization computation and intensity correction for prior information complexity, this method can be considerably time-consuming. Parallel Generalized Series Imaging uses a prior-information-driven method to generate an approximated reconstruction image for a more accurate sensitivity map, and then applies this sensitivity map and a generalized SENSE method to produce a better reconstruction (Liang, et al. (22,23)). In contrast to the disclosure of U.S. Pat. No. 6,448,771 and the teachings of Tsao et al. (Tsao, Jeffrey, Behnia, Babak, Tsao B B, Andrew G. Webb (2001), “Unifying Linear Prior-Information-Driven Methods for Accelerated Image Acquisition”, Magn. Reson. Med., 46:652–660), which copy the prior k-space, and in contrast to (Katscher, U. (2003), “Underdetermined variable density SENSE”, ISMRM, Toronto. p 2342 (21)), which works in image space, the subject method for generating dynamic magnetic resonance images can use the prior information in image space to calibrate the unsampled k-space data.
These strategies are able to reduce data acquisition without compromising image quality significantly because typical images exhibit a high degree of spatial and/or temporal correlations, either by nature or by design. Therefore, there is a certain amount of redundancy within the data. Each of these techniques exploits the correlations in certain ways and can generate high quality images. However, each of these techniques also has drawbacks.
Parallel imaging techniques using multiple coils have become increasingly important since the late 1980's due to higher signal to noise ratios (compared to volume coils or large surface coils) and reduced MRI acquisition time. However, both image-space-based methods (SENSE) and k-space based methods (GRAPPA) only exploit spatial correlations. Methods utilizing k-t-t space based reconstruction techniques take advantage of the temporal correlations, but do not take advantage of the spatial correlations when multi-channel coils are available. K-t space parallel imaging techniques can utilize both spatial and temporal correlations. However, because of the linearity of the existing methods, k-t space parallel imaging techniques cannot utilize non-linear constraints. POCS methods have the advantage that they offer a straightforward and computationally efficient way to incorporate non-linear constraints into the reconstruction that can lead to improved image quality and/or reliable reconstruction for underdetermined problems. Nevertheless the existing POCS based methods do not explicitly exploit either the spatial or temporal correlation.
Hence, there is a need in the art for a method that can combine the benefits of the POCS method with the benefits of parallel imaging and/or the benefits of k-t space reconstruction.